{"cells":[{"cell_type":"markdown","metadata":{},"source":["现给到北京线上某款视频APP在2018年1月-2018年7月的实际用户数据，需要预测2018年8月-2019年12月的数据，请基于课程中的案例分析，建立分析方案并给到预测的数据结果。"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","import matplotlib.pyplot as plt\n","from scipy import stats\n","from scipy import optimize\n","from statsmodels.formula import api as sfm\n","\n","plt.rcParams[\"font.family\"] = \"Microsoft YaHei\""]},{"cell_type":"code","execution_count":2,"metadata":{},"outputs":[],"source":["# 数据导入和转换\n","ldf = pd.read_csv(\"task2.csv\", encoding=\"gbk\")\n","df = pd.DataFrame(data={\"temp\": [i for i in range(24)]})\n","df = pd.merge(\n","    df,\n","    ldf,\n","    how=\"left\",\n","    left_index=True,\n","    right_index=True,\n",")\n","df[\"year\"] = 2018 + df[\"temp\"] // 12\n","df[\"month\"] = df[\"temp\"] % 12 + 1\n","df[\"date\"] = df[\"year\"].astype(str) + \"-\" + df[\"month\"].astype(str)\n","df.drop(columns=[\"temp\", \"日期\"], inplace=True)\n","df.rename(columns={\"当月实际户数（户）\": \"users\"}, inplace=True)"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":["    users  year  month     date    cha   ch_rate  is_event\n","0   179.0  2018      1   2018-1    NaN       NaN     False\n","1   199.0  2018      2   2018-2   20.0  0.111732     False\n","2   330.0  2018      3   2018-3  131.0  0.658291      True\n","3   450.0  2018      4   2018-4  120.0  0.363636      True\n","4   770.0  2018      5   2018-5  320.0  0.711111      True\n","5   821.0  2018      6   2018-6   51.0  0.066234     False\n","6   863.0  2018      7   2018-7   42.0  0.051157     False\n","7     NaN  2018      8   2018-8    NaN       NaN     False\n","8     NaN  2018      9   2018-9    NaN       NaN     False\n","9     NaN  2018     10  2018-10    NaN       NaN     False\n","10    NaN  2018     11  2018-11    NaN       NaN     False\n","11    NaN  2018     12  2018-12    NaN       NaN     False\n","12    NaN  2019      1   2019-1    NaN       NaN     False\n","13    NaN  2019      2   2019-2    NaN       NaN     False\n","14    NaN  2019      3   2019-3    NaN       NaN     False\n","15    NaN  2019      4   2019-4    NaN       NaN     False\n","16    NaN  2019      5   2019-5    NaN       NaN     False\n","17    NaN  2019      6   2019-6    NaN       NaN     False\n","18    NaN  2019      7   2019-7    NaN       NaN     False\n","19    NaN  2019      8   2019-8    NaN       NaN     False\n","20    NaN  2019      9   2019-9    NaN       NaN     False\n","21    NaN  2019     10  2019-10    NaN       NaN     False\n","22    NaN  2019     11  2019-11    NaN       NaN     False\n","23    NaN  2019     12  2019-12    NaN       NaN     False"],"text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        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<td>9</td>\n      <td>2018-9</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>10</td>\n      <td>2018-10</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>11</td>\n      <td>2018-11</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>12</td>\n      <td>2018-12</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>1</td>\n      <td>2019-1</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>2</td>\n      <td>2019-2</td>\n      <td>NaN</td>\n      <td>NaN</td>\n 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<td>NaN</td>\n      <td>2019</td>\n      <td>8</td>\n      <td>2019-8</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>9</td>\n      <td>2019-9</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>10</td>\n      <td>2019-10</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>11</td>\n      <td>2019-11</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>12</td>\n      <td>2019-12</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{},"execution_count":3}],"source":["# 产品上线后可能存在活动或峰值,需要考虑如何排除\n","# 通过对怎张率筛选,如果增长率超过其几何平均值,则认为当前处于活动中\n","df[\"cha\"] = df.users.diff(1)\n","ldf[\"ch_rate\"] = (df.users - df.users.shift(1)) / df.users.shift(1)\n","df[\"ch_rate\"] = (df.users - df.users.shift(1)) / df.users.shift(1)\n","df[\"is_event\"] = (df.users - df.users.shift(1)) / df.users.shift(1) > np.product(\n","    ldf.ch_rate\n",") ** (1 / len(ldf.ch_rate))\n","df"]},{"cell_type":"code","execution_count":4,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":["([<matplotlib.axis.YTick at 0x1e95a4bc9a0>,\n","  <matplotlib.axis.YTick at 0x1e95a4bceb0>,\n","  <matplotlib.axis.YTick at 0x1e95a51e490>,\n","  <matplotlib.axis.YTick at 0x1e95a7dbcd0>,\n","  <matplotlib.axis.YTick at 0x1e95a7ee700>,\n","  <matplotlib.axis.YTick at 0x1e95a7eec10>,\n","  <matplotlib.axis.YTick at 0x1e95a7f4160>],\n"," [Text(0, 0, ''),\n","  Text(0, 0, ''),\n","  Text(0, 0, ''),\n","  Text(0, 0, ''),\n","  Text(0, 0, ''),\n","  Text(0, 0, ''),\n","  Text(0, 0, 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\n"},"metadata":{"needs_background":"light"}}],"source":["# 图表绘制\n","plt.figure(figsize=(12, 5))\n","plt.scatter(x=df.index, y=df.users)\n","plt.xticks(df.index, df.date, rotation=-90)\n","plt.yticks([i * 500 for i in range(7)])\n","\n",""]},{"cell_type":"markdown","metadata":{},"source":["模型选择\n","+ 自回归\n","+ 线性模型\n","+ 非线性模型\n","    + 指数\n","    + 多项式\n","    + 对数\n","评估指标"]},{"cell_type":"code","execution_count":5,"metadata":{},"outputs":[],"source":["# 评估指标\n","def _statistics(y, y_prodict):\n","    t_res = stats.ttest_rel(y, y_prodict)\n","    f_res = stats.f_oneway(y, y_prodict)\n","    ssr = np.sum((y_prodict - np.mean(y)) ** 2)\n","    sse = np.sum((y - y_prodict) ** 2)\n","    sst = np.sum((y - np.mean(y)) ** 2)\n","    r2 = 1 - sse / sst\n","\n","    MSE = np.mean(np.square(y - y_prodict))\n","    RMSE = np.sqrt(np.mean(np.square(y - y_prodict)))\n","    MAE = np.mean(np.abs(y - y_prodict))\n","    MAPE = np.mean(np.abs((y - y_prodict) / y)) * 100\n","    return {\n","        \"t_test\": t_res,\n","        \"ANOVA\": f_res,\n","        \"r^2\": {\"r^2\": r2, \"sse\": sse, \"sst\": sst, \"ssr\": ssr},\n","        \"other\": {\"MSE\": MSE, \"RMSE\": RMSE, \"MAE\": MAE, \"MAPE\": MAPE},\n","    }\n","\n",""]},{"cell_type":"code","execution_count":6,"metadata":{},"outputs":[],"source":["def linerfit(model, y_prodict, s=\"\"):\n","    plt.figure(figsize=(12, 5))\n","    plt.scatter(x=df.index, y=df.users)\n","    plt.plot(t.index, y_prodict, c=\"r\", linestyle=\":\", marker=\"o\")\n","    plt.xticks(df.index, df.date, rotation=-90)\n","    ticker_r = [i * 500 for i in range(7)]\n","    plt.yticks([i * 500 for i in range(7)])\n","    plt.text(0, max(ticker_r) / 2, s=s.format(model), fontsize=14)\n","    return _statistics(t.users, y_prodict)\n","\n","\n","t = df[[\"users\", \"year\", \"is_event\"]].dropna()\n","t.reset_index(inplace=True)"]},{"cell_type":"markdown","metadata":{},"source":["三元哑变量回归未能通过模型的假设检验,多个指标t检验未能通过\n","进行向后剔除"]},{"cell_type":"code","execution_count":7,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.994\n","Model:                            OLS   Adj. R-squared:                  0.983\n","Method:                 Least Squares   F-statistic:                     89.63\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):             0.0111\n","Time:                        14:34:37   Log-Likelihood:                -31.080\n","No. Observations:                   7   AIC:                             72.16\n","Df Residuals:                       2   BIC:                             71.89\n","Df Model:                           4                                         \n","Covariance Type:            nonrobust                                         \n","====================================================================================\n","                       coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------------\n","Intercept           48.5682     33.077      1.468      0.280     -93.751     190.887\n","is_event[T.True]    50.8182     32.727      1.553      0.261     -89.996     191.632\n","index ^ 3           30.4773     14.961      2.037      0.179     -33.896      94.850\n","index ^ 2            5.4091     16.364      0.331      0.772     -64.998      75.816\n","index              107.7955      9.484     11.366      0.008      66.987     148.603\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   2.448\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.382\n","Skew:                          -0.175   Prob(JB):                        0.826\n","Kurtosis:                       1.911   Cond. No.                         19.1\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.994</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.983</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   89.63</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th>  <td>0.0111</td> \n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:37</td>     <th>  Log-Likelihood:    </th> <td> -31.080</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   72.16</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     2</td>      <th>  BIC:               </th> <td>   71.89</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th>        <td>   48.5682</td> <td>   33.077</td> <td>    1.468</td> <td> 0.280</td> <td>  -93.751</td> <td>  190.887</td>\n</tr>\n<tr>\n  <th>is_event[T.True]</th> <td>   50.8182</td> <td>   32.727</td> <td>    1.553</td> <td> 0.261</td> <td>  -89.996</td> <td>  191.632</td>\n</tr>\n<tr>\n  <th>index ^ 3</th>        <td>   30.4773</td> <td>   14.961</td> <td>    2.037</td> <td> 0.179</td> <td>  -33.896</td> <td>   94.850</td>\n</tr>\n<tr>\n  <th>index ^ 2</th>        <td>    5.4091</td> <td>   16.364</td> <td>    0.331</td> <td> 0.772</td> <td>  -64.998</td> <td>   75.816</td>\n</tr>\n<tr>\n  <th>index</th>            <td>  107.7955</td> <td>    9.484</td> <td>   11.366</td> <td> 0.008</td> <td>   66.987</td> <td>  148.603</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   2.448</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.382</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td>-0.175</td> <th>  Prob(JB):          </th> <td>   0.826</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.911</td> <th>  Cond. No.          </th> <td>    19.1</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":7}],"source":["model = sfm.ols(formula=\"users~index^3+index^2+index+is_event\", data=t).fit()\n","model.summary()"]},{"cell_type":"markdown","metadata":{},"source":["是否参与活动任然未能通过\n","进行向后剔除"]},{"cell_type":"code","execution_count":8,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.994\n","Model:                            OLS   Adj. R-squared:                  0.988\n","Method:                 Least Squares   F-statistic:                     169.9\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):           0.000758\n","Time:                        14:34:37   Log-Likelihood:                -31.266\n","No. Observations:                   7   AIC:                             70.53\n","Df Residuals:                       3   BIC:                             70.32\n","Df Model:                           3                                         \n","Covariance Type:            nonrobust                                         \n","====================================================================================\n","                       coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------------\n","Intercept           50.7656     27.169      1.868      0.158     -35.699     137.230\n","is_event[T.True]    47.4375     26.068      1.820      0.166     -35.521     130.396\n","index ^ 3           34.7031      6.517      5.325      0.013      13.963      55.443\n","index              108.6406      7.658     14.186      0.001      84.269     133.013\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   2.492\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.768\n","Skew:                           0.013   Prob(JB):                        0.681\n","Kurtosis:                       1.378   Cond. No.                         14.7\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.994</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.988</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   169.9</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th> <td>0.000758</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:37</td>     <th>  Log-Likelihood:    </th> <td> -31.266</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   70.53</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     3</td>      <th>  BIC:               </th> <td>   70.32</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th>        <td>   50.7656</td> <td>   27.169</td> <td>    1.868</td> <td> 0.158</td> <td>  -35.699</td> <td>  137.230</td>\n</tr>\n<tr>\n  <th>is_event[T.True]</th> <td>   47.4375</td> <td>   26.068</td> <td>    1.820</td> <td> 0.166</td> <td>  -35.521</td> <td>  130.396</td>\n</tr>\n<tr>\n  <th>index ^ 3</th>        <td>   34.7031</td> <td>    6.517</td> <td>    5.325</td> <td> 0.013</td> <td>   13.963</td> <td>   55.443</td>\n</tr>\n<tr>\n  <th>index</th>            <td>  108.6406</td> <td>    7.658</td> <td>   14.186</td> <td> 0.001</td> <td>   84.269</td> <td>  133.013</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   2.492</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.768</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.013</td> <th>  Prob(JB):          </th> <td>   0.681</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.378</td> <th>  Cond. No.          </th> <td>    14.7</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":8}],"source":["model = sfm.ols(formula=\"users~index^3+index+is_event\", data=t).fit()\n","model.summary()"]},{"cell_type":"markdown","metadata":{},"source":["各项指标接近通过,只有截距未能通过\n","绘图检验后发现模型偏离非常严重,不建议使用"]},{"cell_type":"code","execution_count":9,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.988\n","Model:                            OLS   Adj. R-squared:                  0.982\n","Method:                 Least Squares   F-statistic:                     160.5\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):           0.000152\n","Time:                        14:34:37   Log-Likelihood:                -33.869\n","No. Observations:                   7   AIC:                             73.74\n","Df Residuals:                       4   BIC:                             73.58\n","Df Model:                           2                                         \n","Covariance Type:            nonrobust                                         \n","==============================================================================\n","                 coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------\n","Intercept     76.1786     29.275      2.602      0.060      -5.103     157.460\n","index ^ 3     30.7500      7.718      3.984      0.016       9.321      52.179\n","index        111.4643      9.420     11.832      0.000      85.309     137.619\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   1.558\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.521\n","Skew:                          -0.371   Prob(JB):                        0.771\n","Kurtosis:                       1.889   Cond. No.                         10.5\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.988</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.982</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   160.5</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th> <td>0.000152</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:37</td>     <th>  Log-Likelihood:    </th> <td> -33.869</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   73.74</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     4</td>      <th>  BIC:               </th> <td>   73.58</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th> <td>   76.1786</td> <td>   29.275</td> <td>    2.602</td> <td> 0.060</td> <td>   -5.103</td> <td>  157.460</td>\n</tr>\n<tr>\n  <th>index ^ 3</th> <td>   30.7500</td> <td>    7.718</td> <td>    3.984</td> <td> 0.016</td> <td>    9.321</td> <td>   52.179</td>\n</tr>\n<tr>\n  <th>index</th>     <td>  111.4643</td> <td>    9.420</td> <td>   11.832</td> <td> 0.000</td> <td>   85.309</td> <td>  137.619</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   1.558</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.521</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td>-0.371</td> <th>  Prob(JB):          </th> <td>   0.771</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.889</td> <th>  Cond. 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= (\n","    model.params[0] + model.params[1] * t.index ** 3 + model.params[2] * t.index\n",")\n","linerfit(\n","    model.params, t.prodict, s=\"users={0[0]: .2f} + {0[1]: .2f}index^3+{0[2]: .2f}index\"\n",")\n","plt.figure(figsize=(12, 5))\n","plt.scatter(x=t.index, y=t.users - t[\"prodict\"])"]},{"cell_type":"code","execution_count":11,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.974\n","Model:                            OLS   Adj. R-squared:                  0.961\n","Method:                 Least Squares   F-statistic:                     75.65\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):           0.000663\n","Time:                        14:34:39   Log-Likelihood:                -36.454\n","No. Observations:                   7   AIC:                             78.91\n","Df Residuals:                       4   BIC:                             78.75\n","Df Model:                           2                                         \n","Covariance Type:            nonrobust                                         \n","==============================================================================\n","                 coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------\n","Intercept     84.4675     42.012      2.011      0.115     -32.176     201.111\n","index ^ 2     27.3409     11.661      2.345      0.079      -5.036      59.717\n","index        113.8994     13.838      8.231      0.001      75.479     152.319\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   2.781\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.215\n","Skew:                          -0.333   Prob(JB):                        0.898\n","Kurtosis:                       2.461   Cond. No.                         10.3\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.974</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.961</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   75.65</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th> <td>0.000663</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:39</td>     <th>  Log-Likelihood:    </th> <td> -36.454</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   78.91</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     4</td>      <th>  BIC:               </th> <td>   78.75</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th> <td>   84.4675</td> <td>   42.012</td> <td>    2.011</td> <td> 0.115</td> <td>  -32.176</td> <td>  201.111</td>\n</tr>\n<tr>\n  <th>index ^ 2</th> <td>   27.3409</td> <td>   11.661</td> <td>    2.345</td> <td> 0.079</td> <td>   -5.036</td> <td>   59.717</td>\n</tr>\n<tr>\n  <th>index</th>     <td>  113.8994</td> <td>   13.838</td> <td>    8.231</td> <td> 0.001</td> <td>   75.479</td> <td>  152.319</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   2.781</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.215</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td>-0.333</td> <th>  Prob(JB):          </th> <td>   0.898</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 2.461</td> <th>  Cond. No.          </th> <td>    10.3</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":11}],"source":["model = sfm.ols(formula=\"users~index^2+index\", data=t).fit()\n","model.summary()"]},{"cell_type":"code","execution_count":12,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":["{'t_test': Ttest_relResult(statistic=-2.0965731996072337, pvalue=0.08085991110817795),\n"," 'ANOVA': F_onewayResult(statistic=1.0746934402083839, pvalue=0.3203270188413561),\n"," 'r^2': {'r^2': -1.1994504596517306,\n","  'sse': 1167820.2160566829,\n","  'sst': 530960.0,\n","  'ssr': 2719678.800472273},\n"," 'other': {'MSE': 166831.45943666899,\n","  'RMSE': 408.4500696984504,\n","  'MAE': 292.606679035252,\n","  'MAPE': 48.03899651566869}}"]},"metadata":{},"execution_count":12},{"output_type":"display_data","data":{"text/plain":"<Figure size 864x360 with 1 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\n"},"metadata":{"needs_background":"light"}}],"source":["t[\"prodict\"] = (\n","    model.params[0] + model.params[1] * t.index ** 2 + model.params[2] * t.index\n",")\n","plt.figure(figsize=(12, 5))\n","plt.scatter(x=t.index, y=t.users - t[\"prodict\"])\n","linerfit(model.params, t[\"prodict\"], \"一元y={0[0]:.2f}+{0[1]:.2f}x^2+{0[2]:.2f}x\")"]},{"cell_type":"code","execution_count":13,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.942\n","Model:                            OLS   Adj. R-squared:                  0.914\n","Method:                 Least Squares   F-statistic:                     32.69\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):            0.00332\n","Time:                        14:34:41   Log-Likelihood:                -39.274\n","No. Observations:                   7   AIC:                             84.55\n","Df Residuals:                       4   BIC:                             84.39\n","Df Model:                           2                                         \n","Covariance Type:            nonrobust                                         \n","==========================================================================================\n","                             coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------------------\n","Intercept                104.6104     63.732      1.641      0.176     -72.337     281.558\n","index                    132.6883     16.601      7.993      0.001      86.596     178.781\n","index:is_event[T.True]    10.3636     21.042      0.493      0.648     -48.059      68.786\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   1.793\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.850\n","Skew:                           0.221   Prob(JB):                        0.654\n","Kurtosis:                       1.351   Cond. No.                         7.75\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.942</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.914</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   32.69</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th>  <td>0.00332</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:41</td>     <th>  Log-Likelihood:    </th> <td> -39.274</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   84.55</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     4</td>      <th>  BIC:               </th> <td>   84.39</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n             <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th>              <td>  104.6104</td> <td>   63.732</td> <td>    1.641</td> <td> 0.176</td> <td>  -72.337</td> <td>  281.558</td>\n</tr>\n<tr>\n  <th>index</th>                  <td>  132.6883</td> <td>   16.601</td> <td>    7.993</td> <td> 0.001</td> <td>   86.596</td> <td>  178.781</td>\n</tr>\n<tr>\n  <th>index:is_event[T.True]</th> <td>   10.3636</td> <td>   21.042</td> <td>    0.493</td> <td> 0.648</td> <td>  -48.059</td> <td>   68.786</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   1.793</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.850</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.221</td> <th>  Prob(JB):          </th> <td>   0.654</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.351</td> <th>  Cond. No.          </th> <td>    7.75</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":13}],"source":["model = sfm.ols(formula=\"users~index/is_event\", data=t).fit()\n","model.summary()"]},{"cell_type":"code","execution_count":14,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.939\n","Model:                            OLS   Adj. R-squared:                  0.908\n","Method:                 Least Squares   F-statistic:                     30.71\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):            0.00374\n","Time:                        14:34:41   Log-Likelihood:                -39.480\n","No. Observations:                   7   AIC:                             84.96\n","Df Residuals:                       4   BIC:                             84.80\n","Df Model:                           2                                         \n","Covariance Type:            nonrobust                                         \n","====================================================================================\n","                       coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------------\n","Intercept          115.2143     68.106      1.692      0.166     -73.877     304.305\n","is_event[T.True]     1.1667     68.811      0.017      0.987    -189.884     192.217\n","index              133.4286     17.026      7.837      0.001      86.156     180.701\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   1.935\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.857\n","Skew:                           0.599   Prob(JB):                        0.651\n","Kurtosis:                       1.774   Cond. No.                         8.99\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.939</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.908</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   30.71</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th>  <td>0.00374</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:41</td>     <th>  Log-Likelihood:    </th> <td> -39.480</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   84.96</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     4</td>      <th>  BIC:               </th> <td>   84.80</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th>        <td>  115.2143</td> <td>   68.106</td> <td>    1.692</td> <td> 0.166</td> <td>  -73.877</td> <td>  304.305</td>\n</tr>\n<tr>\n  <th>is_event[T.True]</th> <td>    1.1667</td> <td>   68.811</td> <td>    0.017</td> <td> 0.987</td> <td> -189.884</td> <td>  192.217</td>\n</tr>\n<tr>\n  <th>index</th>            <td>  133.4286</td> <td>   17.026</td> <td>    7.837</td> <td> 0.001</td> <td>   86.156</td> <td>  180.701</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   1.935</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.857</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.599</td> <th>  Prob(JB):          </th> <td>   0.651</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.774</td> <th>  Cond. No.          </th> <td>    8.99</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":14}],"source":["model = sfm.ols(formula=\"users~index + is_event\", data=t).fit()\n","model.summary()"]},{"cell_type":"code","execution_count":15,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["{'t_test': Ttest_relResult(statistic=-8.031425095730656e-16, pvalue=0.9999999999999993),\n"," 'ANOVA': F_onewayResult(statistic=2.797963436614649e-31, pvalue=1.0),\n"," 'r^2': {'r^2': 0.9388450031210315,\n","  'sse': 32470.85714285715,\n","  'sst': 530960.0,\n","  'ssr': 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exp_func(x, a, b):\n","    return a * np.exp(-b * x)\n","\n","\n","exp_model, modle_cov = optimize.curve_fit(exp_func, t.index, t.users)\n","exp_model\n","exp_model, modle_cov\n","y_prodict = np.array([exp_func(i, exp_model[0], exp_model[1]) for i in range(7)])\n","linerfit(\n","    exp_model,\n","    y_prodict,\n","    s=\"指数 y={0[0]:.2f}e^({0[1]:.2f}x)\",\n",")\n","\n","plt.figure(figsize=(12, 5))\n","plt.scatter(x=t.index, y=t.users - y_prodict)\n",""]},{"cell_type":"markdown","metadata":{},"source":["+ 经过测试\n","    + 发现还是一般线性回归拟合效果较好\n","    + 虽然多项式回归(3次)的拟合度更高,但是由于属于强行拟合因此后续会造成较大偏差,不与使用\n","    + 怎张率并不稳定所以也无法作为参考列\n","    + 哑变量回归 is_event 未能通过模型检验,且R^2提升较少,因此也已于剔除模型\n","    + 残差分布情况,线性回归的残差分布相较于其他模型更为集中,效果更好\n","+ 最终确认模型采用\n","+ $ user_prodict = 115.7143 + 133.4286x $\n","\n","{'t_test': Ttest_relResult(statistic=-8.031425095730656e-16, pvalue=0.9999999999999993),\n"," 'ANOVA': F_onewayResult(statistic=2.797963436614649e-31, pvalue=1.0),\n"," 'r^2': {'r^2': 0.9388450031210315,\n","  'sse': 32470.85714285715,\n","  'sst': 530960.0,\n","  'ssr': 498489.14285714296},\n"," 'other': {'MSE': 4638.693877551022,\n","  'RMSE': 68.10795752003595,\n","  'MAE': 63.42857142857144,\n","  'MAPE': 16.804138516363036}}\n",""]},{"cell_type":"code","execution_count":17,"metadata":{},"outputs":[{"output_type":"stream","name":"stderr","text":["D:\\Anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 7 samples were given.\n  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"]},{"output_type":"execute_result","data":{"text/plain":["<class 'statsmodels.iolib.summary.Summary'>\n","\"\"\"\n","                            OLS Regression Results                            \n","==============================================================================\n","Dep. Variable:                  users   R-squared:                       0.939\n","Model:                            OLS   Adj. R-squared:                  0.927\n","Method:                 Least Squares   F-statistic:                     76.76\n","Date:                Thu, 17 Jun 2021   Prob (F-statistic):           0.000321\n","Time:                        14:34:43   Log-Likelihood:                -39.480\n","No. Observations:                   7   AIC:                             82.96\n","Df Residuals:                       5   BIC:                             82.85\n","Df Model:                           1                                         \n","Covariance Type:            nonrobust                                         \n","==============================================================================\n","                 coef    std err          t      P>|t|      [0.025      0.975]\n","------------------------------------------------------------------------------\n","Intercept    115.7143     54.910      2.107      0.089     -25.437     256.866\n","index        133.4286     15.229      8.761      0.000      94.280     172.577\n","==============================================================================\n","Omnibus:                          nan   Durbin-Watson:                   1.941\n","Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.859\n","Skew:                           0.611   Prob(JB):                        0.651\n","Kurtosis:                       1.796   Cond. No.                         6.85\n","==============================================================================\n","\n","Notes:\n","[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n","\"\"\""],"text/html":"<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>          <td>users</td>      <th>  R-squared:         </th> <td>   0.939</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.927</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   76.76</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Thu, 17 Jun 2021</td> <th>  Prob (F-statistic):</th> <td>0.000321</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>14:34:43</td>     <th>  Log-Likelihood:    </th> <td> -39.480</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>     7</td>      <th>  AIC:               </th> <td>   82.96</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>     5</td>      <th>  BIC:               </th> <td>   82.85</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>Intercept</th> <td>  115.7143</td> <td>   54.910</td> <td>    2.107</td> <td> 0.089</td> <td>  -25.437</td> <td>  256.866</td>\n</tr>\n<tr>\n  <th>index</th>     <td>  133.4286</td> <td>   15.229</td> <td>    8.761</td> <td> 0.000</td> <td>   94.280</td> <td>  172.577</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   1.941</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.859</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.611</td> <th>  Prob(JB):          </th> <td>   0.651</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 1.796</td> <th>  Cond. No.          </th> <td>    6.85</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."},"metadata":{},"execution_count":17}],"source":["model = sfm.ols(formula=\"users~index\", data=t).fit()\n","model.summary()"]},{"cell_type":"code","execution_count":18,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":["    users  year  month     date    cha   ch_rate  is_event      prodict\n","0   179.0  2018      1   2018-1    NaN       NaN     False   115.714286\n","1   199.0  2018      2   2018-2   20.0  0.111732     False   249.142857\n","2   330.0  2018      3   2018-3  131.0  0.658291      True   382.571429\n","3   450.0  2018      4   2018-4  120.0  0.363636      True   516.000000\n","4   770.0  2018      5   2018-5  320.0  0.711111      True   649.428571\n","5   821.0  2018      6   2018-6   51.0  0.066234     False   782.857143\n","6   863.0  2018      7   2018-7   42.0  0.051157     False   916.285714\n","7     NaN  2018      8   2018-8    NaN       NaN     False  1049.714286\n","8     NaN  2018      9   2018-9    NaN       NaN     False  1183.142857\n","9     NaN  2018     10  2018-10    NaN       NaN     False  1316.571429\n","10    NaN  2018     11  2018-11    NaN       NaN     False  1450.000000\n","11    NaN  2018     12  2018-12    NaN       NaN     False  1583.428571\n","12    NaN  2019      1   2019-1    NaN       NaN     False  1716.857143\n","13    NaN  2019      2   2019-2    NaN       NaN     False  1850.285714\n","14    NaN  2019      3   2019-3    NaN       NaN     False  1983.714286\n","15    NaN  2019      4   2019-4    NaN       NaN     False  2117.142857\n","16    NaN  2019      5   2019-5    NaN       NaN     False  2250.571429\n","17    NaN  2019      6   2019-6    NaN       NaN     False  2384.000000\n","18    NaN  2019      7   2019-7    NaN       NaN     False  2517.428571\n","19    NaN  2019      8   2019-8    NaN       NaN     False  2650.857143\n","20    NaN  2019      9   2019-9    NaN       NaN     False  2784.285714\n","21    NaN  2019     10  2019-10    NaN       NaN     False  2917.714286\n","22    NaN  2019     11  2019-11    NaN       NaN     False  3051.142857\n","23    NaN  2019     12  2019-12    NaN       NaN     False  3184.571429"],"text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>users</th>\n      <th>year</th>\n      <th>month</th>\n      <th>date</th>\n      <th>cha</th>\n      <th>ch_rate</th>\n      <th>is_event</th>\n      <th>prodict</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>179.0</td>\n      <td>2018</td>\n      <td>1</td>\n      <td>2018-1</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>115.714286</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>199.0</td>\n      <td>2018</td>\n      <td>2</td>\n      <td>2018-2</td>\n      <td>20.0</td>\n      <td>0.111732</td>\n      <td>False</td>\n      <td>249.142857</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>330.0</td>\n      <td>2018</td>\n      <td>3</td>\n      <td>2018-3</td>\n      <td>131.0</td>\n      <td>0.658291</td>\n      <td>True</td>\n      <td>382.571429</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>450.0</td>\n      <td>2018</td>\n      <td>4</td>\n      <td>2018-4</td>\n      <td>120.0</td>\n      <td>0.363636</td>\n      <td>True</td>\n      <td>516.000000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>770.0</td>\n      <td>2018</td>\n      <td>5</td>\n      <td>2018-5</td>\n      <td>320.0</td>\n      <td>0.711111</td>\n      <td>True</td>\n      <td>649.428571</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>821.0</td>\n      <td>2018</td>\n      <td>6</td>\n      <td>2018-6</td>\n      <td>51.0</td>\n      <td>0.066234</td>\n      <td>False</td>\n      <td>782.857143</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>863.0</td>\n      <td>2018</td>\n      <td>7</td>\n      <td>2018-7</td>\n      <td>42.0</td>\n      <td>0.051157</td>\n      <td>False</td>\n      <td>916.285714</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>8</td>\n      <td>2018-8</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>1049.714286</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>9</td>\n      <td>2018-9</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>1183.142857</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>NaN</td>\n      <td>2018</td>\n      <td>10</td>\n      <td>2018-10</td>\n      <td>NaN</td>\n      <td>NaN</td>\n   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   <td>2019-3</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>1983.714286</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>4</td>\n      <td>2019-4</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>2117.142857</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>5</td>\n      <td>2019-5</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>2250.571429</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>6</td>\n      <td>2019-6</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>2384.000000</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>NaN</td>\n      <td>2019</td>\n      <td>7</td>\n      <td>2019-7</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>False</td>\n      <td>2517.428571</td>\n    </tr>\n    <tr>\n      <th>19</th>\n   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5))\n","plt.plot(df.index, df.prodict, label=\"预测值\", c=\"r\")\n","plt.text(\n","    0,\n","    df.prodict.max() / 2,\n","    s=\"一元y={0[0]:.2f}x+{0[1]:.2f}\".format(model.params),\n","    fontsize=14,\n","    c=\"r\",\n",")\n","plt.scatter(df.index, df.users)\n","plt.figure(figsize=(12, 5))\n","plt.scatter(x=t.index, y=t.users - t[\"prodict\"])"]},{"cell_type":"markdown","metadata":{},"source":["最终值"]},{"cell_type":"code","execution_count":20,"metadata":{},"outputs":[{"output_type":"execute_result","data":{"text/plain":["       date  users      prodict\n","0    2018-1  179.0   115.714286\n","1    2018-2  199.0   249.142857\n","2    2018-3  330.0   382.571429\n","3    2018-4  450.0   516.000000\n","4    2018-5  770.0   649.428571\n","5    2018-6  821.0   782.857143\n","6    2018-7  863.0   916.285714\n","7    2018-8    NaN  1049.714286\n","8    2018-9    NaN  1183.142857\n","9   2018-10    NaN  1316.571429\n","10  2018-11    NaN  1450.000000\n","11  2018-12    NaN  1583.428571\n","12   2019-1    NaN  1716.857143\n","13   2019-2    NaN  1850.285714\n","14   2019-3    NaN  1983.714286\n","15   2019-4    NaN  2117.142857\n","16   2019-5    NaN  2250.571429\n","17   2019-6    NaN  2384.000000\n","18   2019-7    NaN  2517.428571\n","19   2019-8    NaN  2650.857143\n","20   2019-9    NaN  2784.285714\n","21  2019-10    NaN  2917.714286\n","22  2019-11    NaN  3051.142857\n","23  2019-12    NaN  3184.571429"],"text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>date</th>\n      <th>users</th>\n      <th>prodict</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2018-1</td>\n      <td>179.0</td>\n      <td>115.714286</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2018-2</td>\n      <td>199.0</td>\n      <td>249.142857</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2018-3</td>\n      <td>330.0</td>\n      <td>382.571429</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>2018-4</td>\n      <td>450.0</td>\n      <td>516.000000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2018-5</td>\n      <td>770.0</td>\n      <td>649.428571</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>2018-6</td>\n      <td>821.0</td>\n      <td>782.857143</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>2018-7</td>\n      <td>863.0</td>\n      <td>916.285714</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>2018-8</td>\n      <td>NaN</td>\n      <td>1049.714286</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>2018-9</td>\n      <td>NaN</td>\n      <td>1183.142857</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>2018-10</td>\n      <td>NaN</td>\n      <td>1316.571429</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>2018-11</td>\n      <td>NaN</td>\n      <td>1450.000000</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>2018-12</td>\n      <td>NaN</td>\n      <td>1583.428571</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>2019-1</td>\n      <td>NaN</td>\n      <td>1716.857143</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>2019-2</td>\n      <td>NaN</td>\n      <td>1850.285714</td>\n    </tr>\n    <tr>\n      <th>14</th>\n      <td>2019-3</td>\n      <td>NaN</td>\n      <td>1983.714286</td>\n    </tr>\n    <tr>\n      <th>15</th>\n      <td>2019-4</td>\n      <td>NaN</td>\n      <td>2117.142857</td>\n    </tr>\n    <tr>\n      <th>16</th>\n      <td>2019-5</td>\n      <td>NaN</td>\n      <td>2250.571429</td>\n    </tr>\n    <tr>\n      <th>17</th>\n      <td>2019-6</td>\n      <td>NaN</td>\n      <td>2384.000000</td>\n    </tr>\n    <tr>\n      <th>18</th>\n      <td>2019-7</td>\n      <td>NaN</td>\n      <td>2517.428571</td>\n    </tr>\n    <tr>\n      <th>19</th>\n      <td>2019-8</td>\n      <td>NaN</td>\n      <td>2650.857143</td>\n    </tr>\n    <tr>\n      <th>20</th>\n      <td>2019-9</td>\n      <td>NaN</td>\n      <td>2784.285714</td>\n    </tr>\n    <tr>\n      <th>21</th>\n      <td>2019-10</td>\n      <td>NaN</td>\n      <td>2917.714286</td>\n    </tr>\n    <tr>\n      <th>22</th>\n      <td>2019-11</td>\n      <td>NaN</td>\n      <td>3051.142857</td>\n    </tr>\n    <tr>\n      <th>23</th>\n      <td>2019-12</td>\n      <td>NaN</td>\n      <td>3184.571429</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{},"execution_count":20}],"source":["df[['date','users','prodict']]"]}],"nbformat":4,"nbformat_minor":2,"metadata":{"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":3},"orig_nbformat":4}}